Shock Waves

, Volume 20, Issue 2, pp 163–173 | Cite as

Effect of initial disturbance on the detonation front structure of a narrow duct

Original Article
First Online:
Received:
Revised:
Accepted:

Abstract

The effect of an initial disturbance on the detonation front structure in a narrow duct is studied by three-dimensional numerical simulation. The numerical method used includes a high-resolution fifth-order weighted essentially non-oscillatory scheme for spatial discretization, coupled with a third-order total variation diminishing Runge-Kutta time-stepping method. Two types of disturbances are used for the initial perturbation. One is a random disturbance which is imposed on the whole area of the detonation front, and the other is a symmetrical disturbance imposed within a band along the diagonal direction on the front. The results show that the two types of disturbances lead to different processes. For the random disturbance, the detonation front evolves into a stable spinning detonation. For the symmetrical diagonal disturbance, the detonation front displays a diagonal pattern at an early stage, but this pattern is unstable. It breaks down after a short while and it finally evolves into a spinning detonation. The spinning detonation structure ultimately formed due to the two types of disturbances is the same. This means that spinning detonation is the most stable mode for the simulated narrow duct. Therefore, in a narrow duct, triggering a spinning detonation can be an effective way to produce a stable detonation as well as to speed up the deflagration to detonation transition process.

Keywords

Detonation physics Three-dimensional Simulation Spinning Initial disturbance 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kailasanath K.: Review of propulsion applications of detonation waves. AIAA J. 38, 1698–1708 (2000)CrossRefGoogle Scholar
  2. 2.
    Roy G.D., Frolov S.M., Borisov A.A., Netzer D.W.: Pulse detonation propulsion: challenges, current status, and future perspective. Prog. Energy Combust. Sci. 30, 545–672 (2004)CrossRefGoogle Scholar
  3. 3.
    Lee, J.H.S.: The propagation mechanism of cellular detonation. In: Jiang, Z. (ed.) Shock Waves: Proceedings of the 24th International Symposium on Shock Waves, vol. 1, pp. 19–30. Springer, BerlinGoogle Scholar
  4. 4.
    Mitrofanov V.V.: Modern View of Gaseous Detonation Mechanism, Progress in Astronautics and Aeronautics, vol. 137. Washington DC, AIAA (1996)Google Scholar
  5. 5.
    Lu, F., Bellini, R.: Progress in modeling pulse detonations. Lecture Notes in Workshop on Moving Interface Problems and Applications in Fluid Dynamics, 8 Jan–31 Mar, IMS, NUS (2007)Google Scholar
  6. 6.
    Taki S., Fujiwara T.: Numerical analysis of two dimensional nonsteady detonations. AIAA J. 16, 73–77 (1978)CrossRefGoogle Scholar
  7. 7.
    Oran E., Young T., Boris J.: Application of time-dependent numerical methods to the description of reactive shocks. Proc. Combust. Inst. 17, 43–54 (1978)Google Scholar
  8. 8.
    Kailasanath K., Oran E.S., Boris J.P., Young T.R.: Determination of detonation cell size and the role of transverse waves in two-dimensional detonations. Combust. Flame 61, 199–209 (1985)CrossRefGoogle Scholar
  9. 9.
    Bourlioux A., Majda A.J.: Theoretical and numerical structure of unstable detonations. Philos. Trans. Roy. Soc. London Ser. A 350, 29–68 (1995)MATHCrossRefGoogle Scholar
  10. 10.
    Gamezo V.N., Desbordes D., Oran E.S.: Formation and evolution of two-dimensional cellular detonations. Combust. Flame 116, 154–165 (1999)CrossRefGoogle Scholar
  11. 11.
    Sharpe G.J.: Transverse waves in numerical simulations of cellular detonations. J. Fluid Mech. 447, 31–51 (2001)MATHMathSciNetGoogle Scholar
  12. 12.
    Oran E.S., Weber J.E., Stefaniw E.I., Lefebvre M.H., Anderson J.D.: A numerical study of two-dimensional H2–O2–Ar detonation using a detailed chemical reaction model. Combust. Flame 113, 147–163 (1998)CrossRefGoogle Scholar
  13. 13.
    Hu X.Y., Khoo B.C., Zhang D.L., Jiang Z.L.: The cellular structure of a two-dimensional H-2/O-2/Ar detonation wave. Combust. Theory Model. 8, 339–359 (2004)CrossRefGoogle Scholar
  14. 14.
    Fan H.Y., Lu F.K.: Comparison of detonation processes in a variable cross-section chamber and a simple tube. J. Propul. Power 21(1), 65–75 (2005)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Fan H.Y., Lu F.K.: Numerical simulation of detonation processes in a variable cross-section chamber. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 222(5), 673–686 (2008)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Qu Q., Khoo B.C., Dou H.-S., Tsai H.M.: The evolution of a detonation wave in a variable cross-sectional chamber. Shock Waves 18, 213–233 (2008)MATHCrossRefGoogle Scholar
  17. 17.
    Williams D.N., Bauwens L., Oran E.S.: Detailed structure and propagation of three-dimensional detonations. Proc. Combust. Inst. 26, 2991–2998 (1997)Google Scholar
  18. 18.
    Tsuboi N., Katoh S., Hayashi A.K.: Three-dimensional numerical simulation for hydrogen/air detonation: rectangular and diagonal structures. Proc. Combust. Inst. 29, 2783–2788 (2002)CrossRefGoogle Scholar
  19. 19.
    Deiterding R., Bader G.: High-resolution simulation of detonations with detailed chemistry. In: Warnecke, G. (eds) Analysis and Numerics for Conservation Laws, pp. 69–91. Springer, Berlin (2005)CrossRefGoogle Scholar
  20. 20.
    He, H., Yu, S.T.J., Zhang, Z.-C.: Direct Calculations of One-, Two-, and Three-dimensional detonations by the CESE method, AIAA Paper 2005-0229 (2005)Google Scholar
  21. 21.
    Eto K., Tsuboi N., Hayashi A.K.: Numerical study on three-dimensional C-J detonation waves: detailed propagating mechanism and existence of OH radical. Proc. Combust. Inst. 30, 1907–1913 (2005)CrossRefGoogle Scholar
  22. 22.
    Deledicque V., Papalexandris M.V.: Computational study of three-dimensional gaseous detonation structures. Combust. Flame 144, 821–837 (2006)CrossRefGoogle Scholar
  23. 23.
    Dou H.-S., Tsai H.M., Khoo B.C., Qiu J.: Simulations of detonation wave propagation in rectangular ducts using a three-dimensional WENO scheme. Combust. Flame 154, 644–659 (2008)CrossRefGoogle Scholar
  24. 24.
    Hanana M., Lefebvre M.H., Van Tiggelen P.J.: Pressure profiles in detonation cells with rectangular and diagonal structures. Shock Waves 11, 77–88 (2001)CrossRefGoogle Scholar
  25. 25.
    Tsuboi N., Hayashi A.K.: Numerical study on spinning detonations. Proc. Combust. Inst. 31, 2389–2396 (2007)CrossRefGoogle Scholar
  26. 26.
    Schott G.L.: Observations of the structure of spinning detonation waves. Phys. Fluids 8, 850–865 (1965)CrossRefGoogle Scholar
  27. 27.
    Zhang F., Gronig H.: Spin detonation in reactive particles-oxidizing gas flow. Phys. Fluids A 3(8), 1983–1990 (1991)CrossRefGoogle Scholar
  28. 28.
    Ishii K., Gronig H.: Behavior of detonation waves at low pressures. Shock Waves 8, 55–61 (1998)MATHCrossRefGoogle Scholar
  29. 29.
    Zhang F., Murray S.B., Gerrard K.B.: Aluminium particles-air detonation at elevated pressures. Shock Waves 15, 313–324 (2006)CrossRefGoogle Scholar
  30. 30.
    Huang Z.W., Lefebvre M.H., Van Tiggelen P.J.: Experiments on spinning detonations with detailed analysis of the shock structure. Shock Waves 10, 119–125 (2000)CrossRefGoogle Scholar
  31. 31.
    Mizutani T., Matsui H., Sanui H., Yonekura M.: Decompsoing detonation and deflagration properties of ozone/oxygen mixtures. J. Loss Prev. Process Ind. 14, 559–565 (2001)CrossRefGoogle Scholar
  32. 32.
    Achasov O.V., Penyazkov O.G.: Dynamics study of detonation-wave cellular structure 1.Statistical properties of detonation wave front. Shock Waves 11, 297–308 (2002)CrossRefGoogle Scholar
  33. 33.
    Kasimov A.R., Stewart D.S.: Spinning instability of gaseous detonations. J. Fluid Mech. 466, 179–203 (2002)MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Ivleva T.P., Merzhanov A.G.: Structure and variability of spinning reaction waves in three-dimensional excitable media. Phys. Rev. E 64, 036218 (2001)CrossRefGoogle Scholar
  35. 35.
    Tsuboi N., Asahara M., Eto K., Hayashi A.K.: Numerical simulation of spinning detonation in square tube. Shock Waves 18, 329–344 (2008)MATHCrossRefGoogle Scholar
  36. 36.
    Dou, H.S., Tsai, H.M., Khoo, B.C., Qiu, J.: Three-dimensional simulation of detonation waves using WENO schemes, In: 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8–11 Jan 2007 (AIAA Paper-2006-1177)Google Scholar
  37. 37.
    Vasil’ev A.A.: Cell size as the main geometric parameter of a multifront detonation wave. J. Propul. Power 22, 1245–1260 (2006)CrossRefGoogle Scholar
  38. 38.
    Jiang G.S., Shu C.W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228 (1996)MATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Toro E.F.: Riemann solvers and numerical methods for fluids dynamics. Springer, Berlin (1997)Google Scholar
  40. 40.
    He X., Karagozian A.R.: Numerical simulation of pulse detonation engine phenomena. J. Sci. Comput. 19(1–3), 201–224 (2003)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational University of SingaporeSingaporeSingapore

Personalised recommendations